Understanding Apothem in Equilateral Triangles

The video tutorial explains how to find the length of the apothem in an equilateral triangle. It begins by defining the apothem as the shortest distance from the center to a side of the triangle. The tutorial then demonstrates how to draw strategic lines, including the radius, to form a helpful right triangle. By analyzing the angles, the video shows how to use trigonometric relationships to calculate the apothem's length, given the side length of the triangle. The process involves rationalizing the denominator to simplify the final expression.

What is the apothem in an equilateral triangle?

• The angle bisector of the triangle

• The distance from the center to a vertex

• The longest side of the triangle

• The shortest distance from the center to a side

What is the significance of drawing a radius in the context of this problem?

• It is used to calculate the area of the triangle

• It divides the triangle into two equal parts

• It creates a circle that passes through all vertices

• It helps in finding the perimeter of the triangle

What angle is formed at the center when the radius is drawn?

• 30 degrees

• 45 degrees

• 90 degrees

• 60 degrees

In the right triangle formed, which side is the apothem?

• The hypotenuse

• The base

• The long leg

• The short leg

What is the length of the side of the equilateral triangle before it is divided by the apothem?

• 6 units

• 18 units

• 12 units

• 24 units

What is the relationship between the short leg and the hypotenuse in the right triangle?

• The hypotenuse is three times the short leg

• The hypotenuse is half the short leg

• The hypotenuse is twice the short leg

• The hypotenuse is equal to the short leg

How do you rationalize the denominator in the apothem calculation?

• Multiply by the square root of 2

• Multiply by the square root of 3

• Multiply by the square root of 5

• Multiply by the square root of 6

What is the final simplified length of the apothem?

• 2√3

• 3√2

• 4√3

• 5√2

Why is the apothem considered the shortest distance from the center to a side?

• Because it is perpendicular to the side

• Because it is parallel to the side

• Because it is the longest line possible

• Because it bisects the angle

What is the purpose of finding the apothem in an equilateral triangle?

• To calculate the perimeter

• To find the area

• To understand the symmetry

• To determine the height